Place four pebbles on the sand in the form of a square. Keep adding as few pebbles as necessary to double the area. How many extra pebbles are added each time?
Suppose we allow ourselves to use three numbers less than 10 and
multiply them together. How many different products can you find?
How do you know you've got them all?
Investigate the different shaped bracelets you could make from 18 different spherical beads. How do they compare if you use 24 beads?
Is it possible to draw a 5-pointed star without taking your
pencil off the paper?
Is it possible to draw a $6$-pointed star in the same way
without taking your pen off? Remember that you shouldn't join
points that are right next to each other and you can't go over the
same line twice. Your lines must run straight from one point of the
star to another.
Have a go:
What about $7$-pointed and $8$-pointed stars?
Do you think you'll be able to draw a $9$-pointed star without
taking your pencil off? Why?